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Investing in Volatility

Published in Futures and Options World 1998 Special Supplement on the 25th Annivesary of the Publication of the Black-Scholes Model

In the beginning was the bond, its value measured simply by its price. Soon, analysts invented better mea- sures of relative bond value: current yield, which led to yield to maturity, followed by the term structure of yields, the zero coupon yield curve, and finally forward rates and the forward rate curve. Their importance reflected the fact that these future rates can be locked in, once and for all, using bond portfolios today. From then on, every interest rate trader and analyst carried in his head an abstract forward rate curve.

Thinking in terms of forward rates stimulated the development of new derivative instruments which mir- rored the underlying reality of forward rates; Eurodollar futures contracts and interest rate swaps are just two examples. But as far as the valuation and analysis of these instruments was concerned, the forward rate curve was a deterministic, static parameter whose future evolution had no impact on the current instrument value.

The history of interest rate analysis in the 1980’s and 1990’s has been the story of increasingly successful attempts by modelers to breathe realistic life and movement (that is, volatility) into the evolution of the for- ward rate curve, without violating theoretical arbitrage bounds. As traders’ confidence in these valuation models and their hedges grew, these efforts led to more liquid and better tailored varieties of interest rate caps, swaptions, range notes and related interest rate derivatives whose values depend not only on the yield curve today, but on its volatility as well. Figure 1 contains a schematic history of interest rate modeling.


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